Distribution of Values of Quadratic Forms at Integral Points

The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m : a<Q[m]<b\}$, which are restricted to rescaled and growing domains $r\;\Omega$, is approximated by the volume. An effective error bound of order $o(r^{d-2})$ for this approximation is proved based on Diophantine approximation properties of the quadratic form $Q$. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dimension $d \geq 9$ to dimension $d \geq 5$. They apply to wide shells when $b-a$ is growing with $r$ and to positive definite forms $Q$. For indefinite forms they provide explicit bounds (depending on the signature or Diophantine properties of $Q$) for the size of non-zero integral points $m$ in dimension $d\geq 5$ solving the Diophantine inequality $|Q[m]| < \varepsilon$ and provide error bounds comparable with those for positive forms up to powers of $\log r$.Comment: Section 4 and 7, also bounds in sections 6 have been revised and greatly extended, e.g. box artifacts for wide hyperbolic shells are removed. Applications to Diophantine lattices are revised and reduced exponents for solutions of Diophantine inequalities depending on signature are proved for large $d$, similar to integral forms. For small $d$ larger exponents are now required in Th.1.

Why municipalities grow: The influence of fiscal incentives on municipal land policies in Germany and the Netherlands

It is generally assumed that municipalities attract residents and businesses as a result of intermunicipal competition for tax revenues. This growth-oriented behaviour poses a serious problem considering internationally acknowledged goals to limit land take. Nonetheless, research on how fiscal incentives affect municipal land policies is scarce. Adapting a neoinstitutionalist approach, we compare the two contrasting fiscal systems of Germany and the Netherlands. While clear incentives can be deducted from the different sources of municipal income, complex balancing measurements and consequential infrastructure investments make it difficult to predict a project’s profitability. According to the perspective of planning practitioners in municipalities around the growth centres of Utrecht and Berlin interviewed for this study, local pressures force them to keep allocating new building sites. In order to create effective policies to limit land take, it is important to understand not only the influence of fiscal incentives but also of place-specific pressures on municipal land policies

The role of azacitidine in the management of myelodysplastic syndromes (MDS)

Myelodysplastic syndromes (MDS) are a group of common bone marrow disorders characterized by ineffective hematopoiesis, peripheral cytopenias, and a propensity for transformation to acute myeloid leukemia (AML). For many years, the main treatment option for MDS was best supportive care which alleviates symptoms but has no effect on the natural course of the disease. The recent approval of the demethylating agent azacitidine represents a significant advance in the treatment of MDS. The results of two randomized trials with azacitidine have shown an overall response rate between 40% and 60%, an improved quality of life, a reduced risk of transformation to AML and a definite survival advantage compared to best supportive care or low-dose chemotherapy. Current data on azacitidine and its place in the treatment of MDS are reviewed

On the "generalized Generalized Langevin Equation"

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. In contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation, but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows to relate the Taylor expansion of the memory kernel to data that is accessible in MD simulations and experiments, thus allowing to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions, and is shown to be consistent with direct measurements from simulations

Information structure

The guidelines for Information Structure include instructions for the annotation of Information Status (or ‘givenness’), Topic, and Focus, building upon a basic syntactic annotation of nominal phrases and sentences. A procedure for the annotation of these features is proposed

From Equilibrium to Steady-State Dynamics after Switch-On of Shear

A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.Comment: 16 pages, 12 figures, submitted to Phys Rev